Start by finding the sum of (-8 3/4) and (-2 5/6). Find the least common denominator (LCD). 12 is the first thing that both 4 and 6 will evenly divide into, so we convert both fractions to 12ths:
-8 3/4 = -8 9/12 (multiply 4 by 3 to get 12, so multiply the numerator, 3, by 3 as well)
-2 5/6 = -2 10/12 (multiply 6 by 2 to get 12, so multiply the numerator, 5, by 2 as well)
-8 9/12 + -2 10/12 = -10 19/12
We must convert the improper fraction. 12 goes into 19 1 time with 7 left over, so 19/12 = 1 7/12
This means that -10 19/12 = -11 7/12
The opposite of 1 1/5 is -1 1/5. Add this to -11 7/12. Again find the LCD; in this case it is 60.
-1 1/5 = -1 12/60
-11 7/12 = -11 35/60
Adding these two we get -12 47/60.
Answer:
1) The linear regression model is y = -0.0348·x + 13.989
2) The correlation coefficient is -0.0725
3) The strength of the model is strong - association
Step-by-step explanation:
1)
X Y XY X²
27 13 351 729
65 12 780 4225
83 11 913 6889
109 10 1090 11881
142 9 1278 20164
175 8 1400 30625
∑ 601 63 5812 74513
From y = ax + b, we have
b = 1/n(∑y -a∑x) = 1/6(63 - (0.0348)×601) = 13.989
Therefore, the linear regression model is y = -0.0348·x + 13.989
2)
![r = \frac{n\sum xy - \sum x\sum y }{\sqrt{[n\sum x^{2}-\left (\sum x \right )^{2}] [n\sum y^{2}-\left (\sum y \right )^{2}]}} = \frac{6 \times 5812 - 601 \times 63}{\sqrt{[6 \times 74513-601^{2}] [6 \times 3969 - 63^2]} } = - 0.0725](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bn%5Csum%20xy%20-%20%5Csum%20x%5Csum%20y%20%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E%7B2%7D-%5Cleft%20%28%5Csum%20x%20%20%5Cright%20%29%5E%7B2%7D%5D%20%5Bn%5Csum%20y%5E%7B2%7D-%5Cleft%20%28%5Csum%20y%20%20%5Cright%20%29%5E%7B2%7D%5D%7D%7D%20%20%3D%20%5Cfrac%7B6%20%5Ctimes%205812%20%20-%20601%20%5Ctimes%2063%7D%7B%5Csqrt%7B%5B6%20%5Ctimes%2074513-601%5E%7B2%7D%5D%20%5B6%20%20%5Ctimes%203969%20-%2063%5E2%5D%7D%20%7D%20%3D%20-%200.0725)
3) The strength is - association.
Answer:
The answer is 390 × pi.
Step-by-step explanation:
Big cone:
V = 1/3 x pi x r^2 x h
= 1/3 x 3.14 x 9^2 x 15
= 1272.3 cubic inches
Small cone:
V = 1/3 x pi x r^2 x h
= 1/3 x 3.14 x 3^2 x 5
= 47.1 cubic inches
1272.3 - 47.1 = 1225.2 cubic inches
1272/3.14 ≈ 390
The answer is 390 × pi.
Answer:
2L+2W=P, where L is the length, W is the width, and P is the perimeter.
Step-by-step explanation:
To find the perimeter of a rectangle, you add the length twice and the width twice, which translates to W+W+L+L, or 2L+2W.
